What is the derivative of ({f}(x)(2xe^x)) ?

The derivative of ({f}(x)(2xe^x)) is 2(derivative of {f}(x)xe^x+(e^x+e^xx){f}(x))

What is the first derivative of ({f}(x)(2xe^x)) ?

The first derivative of ({f}(x)(2xe^x)) is 2(derivative of {f}(x)xe^x+(e^x+e^xx){f}(x))

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\frac{d}{d x} ((f (x)) (2 x e^{x}))

2 (\frac{d}{d x} (f (x)) x e^{x} + (e^{x} + e^{x} x) f (x))

Solution steps

\frac{d}{d x} ((f (x)) (2 x e^{x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (f (x) x e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = f (x), g = x e^{x}

= 2 (\frac{d}{d x} (f (x)) x e^{x} + \frac{d}{d x} (x e^{x}) f (x))

\frac{d}{d x} (x e^{x}) = e^{x} + e^{x} x

= 2 (\frac{d}{d x} (f (x)) x e^{x} + (e^{x} + e^{x} x) f (x))

g (- 0.1)

\frac{( 4 x + 5 )}{( 8 x + 10 )}

12 x^{2} - 21 x^{2} + 28 x - 49

e^{2} + 3 e - 28

4 (x)^{2} + 3

What is the derivative of ({f}(x)(2xe^x)) ?
The derivative of ({f}(x)(2xe^x)) is 2(derivative of {f}(x)xe^x+(e^x+e^xx){f}(x))
What is the first derivative of ({f}(x)(2xe^x)) ?
The first derivative of ({f}(x)(2xe^x)) is 2(derivative of {f}(x)xe^x+(e^x+e^xx){f}(x))